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Infinitely many dichotomous solutions for the Schr?dinger-Poisson system

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In this paper,we consider the following Schrödinger-Poisson system {-ε2Δu+V(x)u+K(x)Φ(x)u=|u|p-1u in RN,-ΔΦ(x)=K(x)u2 in RN,where ε is a small parameter,1＜p＜N+2/N-2,N ∈[3,6],and V(x)and K(x)are potential functions with different decay at infinity.We first prove the non-degeneracy of a radial low-energy solution.Moreover,by using the non-degenerate solution,we construct a new type of infinitely many solutions for the above system,which are called"dichotomous solutions",i.e.,these solutions concentrate both in a bounded domain and near infinity.

dichotomous solutionsnon-degeneracySchrödinger-Poisson system

Yuke He、Benniao Li、Wei Long

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School of Mathematics and Statistics and Jiangxi Provincial Center for Applied Mathematics,Jiangxi Normal University,Nanchang 330022,China

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaJiangxi Province Science Fund for Distinguished Young ScholarsNational Natural Science Foundation of ChinaJiangxi Provincial Natural Science FoundationJiangxi Two Thousand Talents ProgramDoublehigh Talents Program in Jiangxi Province

121012741222630920224ACB2180011227122320212ACB201003jxsq2019101001

2024

10.1007/s11425-023-2173-y

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(9)